Thread: Calculus Refresher
A brief review of the concepts of single variable calculus
- Preliminaries
- Differentiation
- The idea of the derivative of a function
- Derivatives of polynomials
- Derivatives of more general power functions
- The quotient rule
- The product rule
- The chain rule
- Tangent and normal lines
- Critical points, monotone increase and decrease
- Minimization and maximization refresher
- Local minima and maxima (First Derivative Test)
- An algebra trick for finding critical points
- Linear approximations: approximation by differentials
- Implicit differentiation
- Related rates
- Intermediate Value Theorem, location of roots
- Newton's Method
- Derivatives of transcendental functions
- L'Hospital's rule
- Exponential growth and decay: a differential equation
- The second and higher derivatives
- Inflection points, concavity upward and downward
- Another differential equation: projectile motion
- Graphing rational functions, asymptotes
- Integration
- Basic integration formulas
- The simplest integration substitutions
- Integration substitutions
- Area and definite integrals
- Length of curves
- Numerical integration
- Averages and weighted averages
- Centers of mass (centroids)
- Volumes by cross sections
- Volume of surfaces of revolution
- Integration by parts
- Partial fractions
- Trigonometric integrals
- Trigonometric substitution
- Taylor polynomials
- Historical and theoretical comments: Mean Value Theorem
- Taylor polynomials: formulas
- Classic examples of Taylor polynomials
- Computational tricks regarding Taylor polynomials
- Prototypes: More serious questions about Taylor polynomials
- Determining tolerance/error in Taylor polynomials.
- How large an interval with given tolerance for a Taylor polynomial?
- Achieving desired tolerance of a Taylor polynomial on desired interval
- Integrating Taylor polynomials: first example
- Integrating the error term of a Taylor polynomial: example
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